Twenty Twelve: Header Image

Yes, you will need to use a Child Theme to do that – so start here:

http://codex.wordpress.org/Child_Themes

get this 150px square image to sit in the header box where the title is, above the Menu and on the right of all pages

Give position relative to .site-header, then position absolute to the .header-image. Be aware that theme is responsive, so make adjustment according to media query.